In this paper, the concept of fuzzy (semi-) topogenous order in the framework of fuzzy topologies, fuzzy proximities and fuzzy uniformities have been introduced. The refinement of fuzzy (semi-) topogenous order has been researched. On this basis, the image and inverse image of refinement of fuzzy (semi-) topogenous order have been defined by general order homomorphism (GOH). Some important properties of them have been obtained.